Dynamic Modality in a Possible Worlds Framework

Abilities – no doubt – have a modal nature, but how to spell out this modal nature is up to debate. In this essay, one approach is of special interest. It could be called the restricted possibility approach to ability. The idea behind the restricted possibility approach is this: There are many kinds of modals which express for example deontic, epistemic or metaphysical modality. But all these di↵erent kinds of modality can be spelled out in one framework. This framework is the usual possible worlds framework where modality is essentially quantification over some set of possible worlds. The di↵erent kinds of modality correspond to di↵erent ways the possible worlds we quantify over are ‘picked out’: deontic modality is quantification over the morally perfect worlds, metaphysical modality quantification over the metaphysically possible worlds and so forth. Abilities however are regarded as another kind of modality, often called dynamic modality (the corresponding modal auxiliary ‘can’ is often referred to as the dynamic ‘can’ or the ‘can’ of ability). To ascribe an ability to someone then, is (in this case existential) quantification over a set of possible worlds. It is an important question what kind of worlds we quantify over when we ascribe abilities to someone but, as we will see, we need not be concerned with this question in this essay. However, Anthony Kenny criticized the restricted possibility approach claiming that there is no way to capture dynamic modality in a standard possible worlds framework (see Kenny [1976]). In this essay my goal is to strengthen his point and show that even some non-standard way to capture the semantics of dynamic modality fails to account for all the peculiarities we face in our talk about abilities. My claim is that we have to give up the closure principle if we want to rely on a possible worlds framework and some prominent interpretation of the operator used to describe dynamic modality. To get to this point I want to proceed as follows: in section 2 I’ll sketch Kennys objection to the restricted possibility approach. This should give a basic impression of the style of critique applied in this essay. In section 3 I want to discuss a reply to